Question

If the probabilities that an automobile mechanic will service 3, 4, 5, 6, 7, or 8 or more cars on any given workday are, respectively, 0.12, 0.19, 0.28, 0.24, 0.10, and 0.07, what is the probability that he will service at least 5 cars on his next day at work?

Answer 1

Answer:

$P(X\geq 5)=0.69$

Step-by-step explanation:

We need to find the probability that the mechanic will service  or more cars.

It's a simpler one given that we have the probabilities of servicing 4 or less cars.

P(at least 5 cars) is given by subtracting the probabilities of servicing both 3 and 4 cars.

$P(X\geq 5)=1-p(x=4)-p(x=3)\\P(X\geq5)=1-0.12-0.19\\P(X\geq5)=1-0.31\\=0.69$